Ceiling – use a 2×6 beam stretched across a few of these roof rafters to support a hammock

400 lbs is not so large (consider that 2 or 3 people standing close to each other could easily exceed that), but you must be careful not to mount the hammock in a way that compromises the joists. Since the hammock supports pull at a diagonal and not straight down, the force exerted at each contact point is actually much more than the weight of the occupants.

It would be best to mount the hammock in the direction of the joists, so that one end is near the outer wall and one end is near the main center beam. The bending load on the joist will be far less than if you mount at the midpoint. Plus, the load from the hammock will be mostly in the axial direction, which is not a big deal.

If you must mount the hammock perpendicular to the joists, suspended from their midpoint, it would be best if the hammock attach point were at the location of cross bracing between the joists, and/or blocking if you have that instead. The bracing prevents the joists from twisting or shifting laterally, which otherwise would be a weakness. If you have no bracing between joists or they're not in a convenient spot, I would add some at the suspension points——say, 2 joists in each direction. If you mount the hammock this way, you must ensure that the joist do not twist or get deflected laterally, as that will severely compromise their stability.

As for attaching to a joist, I would not drill a large hole through the joists if you can avoid it, although it would probably be OK. Try to find a metal bracket at a construction supply store that will fit on the 2x8s and provide a support for your hammock chain. E.g. Home Depot carries several Simpson Strong-Tie products that look promising.

(If this is sounding like too much work or too risky, you could always pick up a free-standing hammock stand.)

The right way to fix this is to have a local engineer size a LVL (laminated veneer lumber) beam for you (solid wood lumber won't meet modern standards for a span that long). It'll likely be taller than your current beam. You'll need to temporarily support all the rafters with a framed wall on each side, using double top plates. Keep them a few feet away from the beam to allow room to work. Remove the existing beam, the posts supporting it, and all metal hangers.

The new beam will likely be 2" thicker than the current one--LVL beams are often 1-3/4" thick per member, and they're usually doubled in cases like this. This will require trimming of the rafters on one or both sides.

Slide the new beam into place and support it a few feet from each end with temporary posts. Fit new posts using adequate lumber. Double 2x4s may be enough, but ask the engineer. Install the same hangers if they're appropriate, or use new ones.

Alternatively, you may be able to install your new beam directly below the existing beam. Of course, this dramatically reduces headroom. I expect a new beam to be sized at around 12" high.